On the Cayleyness of Praeger-Xu graphs

R. Jajcay, P. Potočnik, S. Wilson

Research output: Contribution to journalArticlepeer-review

Abstract

This paper discusses a family of graphs, called Praeger-Xu graphs and denoted PX(n,k) here, introduced by C.E. Praeger and M.-Y. Xu in 1989. These tetravalent graphs are distinguished by having large symmetry groups; their vertex-stabilizers can be arbitrarily larger than the number of vertices in the graph. This paper does the following: (1) exhibits a connection between vertex-transitive groups of symmetries in a Praeger-Xu graph and certain linear codes, (2) characterizes those linear codes, (3) characterizes Praeger-Xu graphs PX(n,k) which are Cayley, (4) shows that every PX(n,k) is quasi-Cayley, and (5) constructs an infinite family of Praeger-Xu graphs in which a smallest vertex-transitive group of symmetries has arbitrarily large vertex-stabiliser.

Original languageEnglish (US)
Pages (from-to)55-79
Number of pages25
JournalJournal of Combinatorial Theory. Series B
Volume152
DOIs
StatePublished - Jan 2022

Keywords

  • Automorphism group
  • Cayley graph
  • Praeger-Xu graph
  • Tetravalent graph
  • Vertex-transitive graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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